SQL Guy 1 (4/10/2013)
It's not necessary to copy backup file from server to server. If your destination SQL server has access to source server, you can restore accross servers, by specifying "...from disk = '\\server\share\file.bak'" or "\\server\C$\folder\file.bak'.This way you will waste less resources.
I'll throw in an "It Depends" here. Depending on your network, it may actually be faster to copy to a local drive then restore than to restore over the network. I had that issue at a couple of previous employers.